# Aptitude - Logarithm

### Exercise :: Logarithm - General Questions

11.

If log 2 = 0.30103, the number of digits in 264 is:

 A. 18 B. 19 C. 20 D. 21

Answer: Option C

Explanation:

 log (264) = 64 x log 2 = (64 x 0.30103) = 19.26592

Its characteristic is 19.

Hence, then number of digits in 264 is 20.

12.

 If logx 9 = - 1 , then x is equal to: 16 2

A.
 - 3 4
B.
 3 4
C.
 81 256
D.
 256 81

Answer: Option D

Explanation:

 logx 9 = - 1 16 2 x-1/2 = 9 16 1 = 9 x 16 x = 16 9 x = 16 2 9 x = 256 81

13.

If ax = by, then:

A.
 log a = x b y
B.
 log a = x log b y
C.
 log a = y log b x
D. None of these

Answer: Option C

Explanation:

ax = by log ax = log by x log a = y log b log a = y . log b x

14.

If logx y = 100 and log2 x = 10, then the value of y is:

 A. 210 B. 2100 C. 21000 D. 210000

Answer: Option C

Explanation:

log 2 x = 10 x = 210. logx y = 100 y = x100 y = (210)100     [put value of x] y = 21000.

15.

The value of log2 16 is:

A.
 1 8
B. 4
C. 8
D. 16

Answer: Option B

Explanation:

Let log2 16 = n.

Then, 2n = 16 = 24 n = 4. log2 16 = 4.

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